Abstract

Nodal aberration theory (NAT) describes the aberration properties of optical systems without symmetry. NAT was fully described mathematically and investigated through real-ray tracing software, but an experimental investigation is yet to be realized. In this study, a two-mirror Ritchey-Chrétien telescope was designed and built, including testing of the mirrors in null configurations, for experimental investigation of NAT. A feature of this custom telescope is a high-precision hexapod that controls the secondary mirror of the telescope to purposely introduce system misalignments and quantify the introduced aberrations interferometrically. A method was developed to capture interferograms for multiple points across the field of view without moving the interferometer. A simulation result of Fringe Zernike coma was generated and analyzed to provide a direct comparison with the experimental results. A statistical analysis of the measurements was conducted to assess residual differences between simulations and experimental results. The interferograms were consistent with the simulations, thus experimentally validating NAT for third-order coma.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Two-mirror telescope design with third-order coma insensitive to decenter misalignment

Lucimara Cristina Nakata Scaduto, Jose Sasian, Mario Antonio Stefani, and Jarbas Caiado de Castro Neto
Opt. Express 21(6) 6851-6865 (2013)

Extending Nodal Aberration Theory to include mount-induced aberrations with application to freeform surfaces

Kyle Fuerschbach, Jannick P. Rolland, and Kevin P. Thompson
Opt. Express 20(18) 20139-20155 (2012)

Misalignment-induced nodal aberration fields in two-mirror astronomical telescopes

Tobias Schmid, Kevin P. Thompson, and Jannick P. Rolland
Appl. Opt. 49(16) D131-D144 (2010)

References

  • View by:
  • |
  • |
  • |

  1. H. H. Hopkins, The Wave Theory of Aberrations (Oxford on Clarendon, 1950).
  2. R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).
    [Crossref]
  3. K. Thompson, “Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry,” J. Opt. Soc. Am. A 22(7), 1389–1401 (2005).
    [Crossref] [PubMed]
  4. K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: spherical aberration,” J. Opt. Soc. Am. A 26(5), 1090–1100 (2009).
    [Crossref] [PubMed]
  5. K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the comatic aberrations,” J. Opt. Soc. Am. A 27(6), 1490–1504 (2010).
    [Crossref] [PubMed]
  6. K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the astigmatic aberrations,” J. Opt. Soc. Am. A 28(5), 821–836 (2011).
    [Crossref] [PubMed]
  7. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” Opt. Express 22(22), 26585–26606 (2014).
    [Crossref] [PubMed]
  8. J. R. Rogers, “Origins and fundamentals of nodal aberration theory,” in Optical Design and Fabrication 2017 (IODC, Freeform, OFT), OSA Technical Digest (online) (Optical Society of America, 2017), paper JTu1C.1.
  9. J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-filed, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
    [Crossref]
  10. R. A. Buchroeder, “Tilted component optical systems,” Ph.D. dissertation (University of Arizona, 1976).
  11. K. P. Thompson, T. Schmid, O. Cakmakci, and J. P. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” J. Opt. Soc. Am. A 26(6), 1503–1517 (2009).
    [Crossref] [PubMed]
  12. D. Malacara, Optical Shop Testing, 3rd ed. (John Wiley & Sons, Inc., 2007), Chap. 12.
  13. T. Yang, J. Zhu, and G. Jin, “Nodal aberration properties of coaxial imaging systems using Zernike polynomial surfaces,” J. Opt. Soc. Am. A 32(5), 822–836 (2015).
    [Crossref] [PubMed]
  14. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992).
  15. J. C. DeBruin and D. B. Johnson, “Image rotation in plane-mirror optical systems,” Proc. SPIE 1696, 41–59 (1992).
  16. CODE V reference manual, Version 11.0, 2017, Synopsys, Inc.
  17. MetroPro manual, Version 9.0, 2011, Zygo Corporation, http://www.zygo.com .
  18. X. Hou, F. Wu, L. Yang, and Q. Chen, “Comparison of annular wavefront interpretation with Zernike circle polynomials and annular polynomials,” Appl. Opt. 45(35), 8893–8901 (2006).
    [Crossref] [PubMed]
  19. T. Schmid, K. P. Thompson, and J. P. Rolland, “A unique astigmatic nodal property in misaligned Ritchey-Chrétien telescopes with misalignment coma removed,” Opt. Express 18(5), 5282–5288 (2010).
    [Crossref] [PubMed]
  20. T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using nodal aberration theory (NAT),” Opt. Express 18(16), 17433–17447 (2010).
    [Crossref] [PubMed]
  21. T. Schmid, “Misalignment induced nodal aberration fields and their use in the alignment of astronomical telescopes,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 2010).

2015 (1)

2014 (1)

2011 (1)

2010 (3)

2009 (2)

2006 (1)

2005 (1)

1992 (1)

J. C. DeBruin and D. B. Johnson, “Image rotation in plane-mirror optical systems,” Proc. SPIE 1696, 41–59 (1992).

1989 (1)

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-filed, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

1980 (1)

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).
[Crossref]

Cakmakci, O.

Chen, Q.

DeBruin, J. C.

J. C. DeBruin and D. B. Johnson, “Image rotation in plane-mirror optical systems,” Proc. SPIE 1696, 41–59 (1992).

Figoski, J. W.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-filed, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

Fuerschbach, K.

Hou, X.

Jin, G.

Johnson, D. B.

J. C. DeBruin and D. B. Johnson, “Image rotation in plane-mirror optical systems,” Proc. SPIE 1696, 41–59 (1992).

Moore, G. F.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-filed, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

Rakich, A.

Rolland, J. P.

Schmid, T.

Shack, R. V.

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).
[Crossref]

Shrode, T. E.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-filed, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

Thompson, K.

Thompson, K. P.

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” Opt. Express 22(22), 26585–26606 (2014).
[Crossref] [PubMed]

K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the astigmatic aberrations,” J. Opt. Soc. Am. A 28(5), 821–836 (2011).
[Crossref] [PubMed]

T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using nodal aberration theory (NAT),” Opt. Express 18(16), 17433–17447 (2010).
[Crossref] [PubMed]

K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the comatic aberrations,” J. Opt. Soc. Am. A 27(6), 1490–1504 (2010).
[Crossref] [PubMed]

T. Schmid, K. P. Thompson, and J. P. Rolland, “A unique astigmatic nodal property in misaligned Ritchey-Chrétien telescopes with misalignment coma removed,” Opt. Express 18(5), 5282–5288 (2010).
[Crossref] [PubMed]

K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: spherical aberration,” J. Opt. Soc. Am. A 26(5), 1090–1100 (2009).
[Crossref] [PubMed]

K. P. Thompson, T. Schmid, O. Cakmakci, and J. P. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” J. Opt. Soc. Am. A 26(6), 1503–1517 (2009).
[Crossref] [PubMed]

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).
[Crossref]

Wu, F.

Yang, L.

Yang, T.

Zhu, J.

Appl. Opt. (1)

J. Opt. Soc. Am. A (6)

Opt. Express (3)

Proc. SPIE (3)

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).
[Crossref]

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-filed, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

J. C. DeBruin and D. B. Johnson, “Image rotation in plane-mirror optical systems,” Proc. SPIE 1696, 41–59 (1992).

Other (8)

CODE V reference manual, Version 11.0, 2017, Synopsys, Inc.

MetroPro manual, Version 9.0, 2011, Zygo Corporation, http://www.zygo.com .

D. Malacara, Optical Shop Testing, 3rd ed. (John Wiley & Sons, Inc., 2007), Chap. 12.

T. Schmid, “Misalignment induced nodal aberration fields and their use in the alignment of astronomical telescopes,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 2010).

R. A. Buchroeder, “Tilted component optical systems,” Ph.D. dissertation (University of Arizona, 1976).

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992).

J. R. Rogers, “Origins and fundamentals of nodal aberration theory,” in Optical Design and Fabrication 2017 (IODC, Freeform, OFT), OSA Technical Digest (online) (Optical Society of America, 2017), paper JTu1C.1.

H. H. Hopkins, The Wave Theory of Aberrations (Oxford on Clarendon, 1950).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1 The aberration field center of third-order coma in a misaligned system is denoted by a131.
Fig. 2
Fig. 2 Full Field Displays (FFDs) of Fringe Zernike coma Z7/8 in a Cassegrain system (a-b) and a Ritchey-Chrétien system (c-d). (a) and (c) are the systems in aligned states. (b) and (d) are the corresponding systems with a 0.5 mm decenter in their secondary mirrors, respectively.
Fig. 3
Fig. 3 Schematic layout of the Hilbert telescope, a Ritchey-Chretien telescope by design.
Fig. 4
Fig. 4 Optical testing of the primary and secondary mirrors: (a) Primary mirror testing scheme (left) and surface figure error (right). (b) Secondary mirror testing scheme (left) and surface figure error (right).
Fig. 5
Fig. 5 Mechanical design model of the SMA assembly and attachment to the primary mirror: (a) Mechanical model of Hilbert telescope; (b) FE analysis result of displacement.
Fig. 6
Fig. 6 The assembled Hilbert telescope.
Fig. 7
Fig. 7 Layout of the experimental setup for field measurements with the Hilbert telescope. The telescope was interfaced with a collimator that generates various points in the field of view of the telescope via a tip/tilt mirror and a retro-reflector that follows where the telescope is focusing.
Fig. 8
Fig. 8 The experiment setup captured during the alignment phase.
Fig. 9
Fig. 9 Alignment of the two interferometers via auto-collimation on a 21 in. optical flat. The Dynafiz had a partially filled aperture. The Verifire was obscured by the hole in the primary and the secondary spiders. In this step of the alignment procedure, the Secondary Mirror Assembly (SMA) was removed.
Fig. 10
Fig. 10 (a) Alignment of the primary mirror of the Hilbert telescope to the reference 21 in. optical flat. (b) Alignment of the secondary mirror to the primary/flat combination.
Fig. 11
Fig. 11 Parabola aligned using the Dynafiz interferometer with a transmission sphere focus from which the beam was then collimated by the parabola, then focused at the focus of the Verifire (set by the transmission sphere of the Verifire) by the telescope, with the Verifire off, and returned. The fold mirrors and parabola were adjusted to remove tip, tilt, defocus, and coma in the Dynafiz interferogram.
Fig. 12
Fig. 12 The experimental setup with a zoom in view on the Hilbert telescope and tip-tilt mirror.
Fig. 13
Fig. 13 Simulated interferograms of coma in (a) aligned state, (b) misaligned state, and (c) subtraction of aligned and misaligned states. The adopted wavelength was 632.8 nm.
Fig. 14
Fig. 14 Experimental results of Fringe Zernike coma in waves units at λ equal 632.8 nm for (a) the aligned system, (b) the misaligned system, and (c) the subtraction of the aligned and misaligned systems.
Fig. 15
Fig. 15 Geometry illustration of (a) a normalized annular aperture with obscuration of ε and (b) is a normalized circular aperture.
Fig. 16
Fig. 16 (a) Statistical analysis of the measurements at field point (−0.1°, −0.1°) in the misaligned state. (b) Standard deviation display of eight consecutive measurement data for that field point reported in three different metrics.

Tables (3)

Tables Icon

Table 1 Specifications of the Hilbert telescope

Tables Icon

Table 2 Main specifications of the hexapod

Tables Icon

Table 3 3x3 grid of field points measured

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

W= j W 040j ( ρρ ) 2 + j W 131j [ ( H σ j )ρ ]( ρρ )+ j W 222j [ ( H σ j )ρ ] 2 + j W 220j [ ( H σ j )( H σ j ) ]( ρρ )+ j W 311j [ ( H σ j )( H σ j ) ] [ ( H σ j )ρ ],
W= j W 131j [ ( H σ j )ρ ]( ρρ )={ [ ( j W 131j H )( j W 131j σ j ) ]ρ } ( ρρ ).
j W 131j H= W 131 H.
A 131 j W 131j σ j ,
a 131 A 131 W 131 ,
W= W 131 [ ( H a 131 )ρ ]( ρρ ).
W=( A 131 ρ )( ρρ ),
| Z 7/8 |= Z 7 2 + Z 8 2 .
Z 7 = 3( 1+ ε 2 ) ρ 3 2( 1+ ε 2 + ε 4 )ρ ( 1 ε 2 ) [ ( 1+ ε 2 )( 1+4 ε 2 + ε 4 ) ] 1/2 cosθ,
Z 8 = 3( 1+ ε 2 ) ρ 3 2( 1+ ε 2 + ε 4 )ρ ( 1 ε 2 ) [ ( 1+ ε 2 )( 1+4 ε 2 + ε 4 ) ] 1/2 sinθ.
Z 7 =ρ( 3 ρ 2 2 )cosθ,
Z 8 =ρ( 3 ρ 2 2 )sinθ.
ξ 7/8 = tan 1 ( Z 8 Z 7 ).

Metrics